leftOp_faithful — Mathlib

English

If F: C ⥤ D^{op} is faithful, then F.leftOp is faithful.

Русский

Если F: C \\\\to D^{op} верен, то F.leftOp верен.

LaTeX

$$$\\\\forall C [\\\\text{Category}(C)], \\\\forall D [\\\\text{Category}(D)], \\\\forall F: C \\\\to D^{op}, \\\\text{Faithful}(F) \\\\Rightarrow \\\\text{Faithful}(F.leftOp).$$$

Lean4

/-- If F is faithful then the left_op of F is also faithful. -/
instance leftOp_faithful {F : C ⥤ Dᵒᵖ} [Faithful F] : Faithful F.leftOp where
  map_injective h := Quiver.Hom.unop_inj (map_injective F (Quiver.Hom.unop_inj h))

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